Electromagnetic Scattering Properties in a Multilayered Metamaterial Cylinder

IEICE TRANS. COMMUN., VOL.E90–B, NO.9 SEPTEMBER 20072423

PAPER Special Section on 2006 International Symposium on Antennas and Propagation

Electromagnetic Scattering Properties in a MultilayeredMetamaterial Cylinder

Cheng-Wei QIU†a), Hai-Ying YAO††b), Shah-Nawaz BUROKUR†††, Saıd ZOUHDI†††c), Nonmembers,and Le-Wei LI††, Member

SUMMARY Electromagnetic scattering properties of metamaterialcylinders due to a line source are studied by a multilayer algorithm basedon eigenfunctional expansion. Closed forms of electric and magnetic fieldsare formulated. Both the fields inside the cylinder and field in outer spaceare plotted for different sizes of the cylinder. The focusing phenomenaand the wave propagation in the presence of metamaterial cylinders areinvestigated and shown. Electromagnetic field distributions are presentedfor subwavelength metamaterial cylinders and cylinders fabricated by mag-netoelectric materials, and resonant scattering and focusing properties arereported. Special designs of scatterer cloaking are proposed and calculatedby multilayer algorithm which can reduce scattering cross sections.key words: multilayer algorithm, metamaterial, magnetoelectric coupling,subwavelength cylinder, cloaking

1. Introduction

The permeability and permittivity of a material are two ofthe fundamental parameters that determine how the materialinteracts with electromagnetic (EM) waves propagating andscattering in the materials. Metamaterials, with simultane-ously negative permittivity and permeability in a frequencyband, have received intensive interests, which exhibit a lotof exotic properties (e.g., reversal Doppler shift and nega-tive refraction [1], reversed circular Bragg phenomenon [2]and perfect lens [3]). These materials exhibit a left-handedrule which are referred to as left-handed materials (LHM) inliterature [4]–[6]. The double negative (DNG) material hasshown special optical properties, and could lead to a perfectlens [7], [8].

The plane wave propagating through layered DNGmedia were formulated by Kong [9] for planar structures.In this paper, existing application is extended to the line-source incidence associated with cylindrical multilayers, soas to gain more insight into the hybrid effects of metama-terials and cylindrical curvature. Eigenfunction expansiontechnique [10]–[12] is employed to establish a systematic

Manuscript received December 26, 2006.Manuscript revised February 17, 2007.†The author is with the Department of Electrical and Com-

puter Engineering, National University of Singapore, and also withEcole Superieure D’Electricite, France.††The authors are with the Department of Electrical and Com-

puter Engineering, National University of Singapore.†††The authors are with the Laboratoire de Genie Electrique de

Paris, Ecole Superieure D’Electricite, France.a) E-mail: chengweiqiu@nus.edu.sgb) E-mail: eleyh (elelilw, eleyeots)@nus.edu.sgc) E-mail: sz@ccr.jussieu.fr

DOI: 10.1093/ietcom/e90–b.9.2423

scheme, which can incorporate the material functionality,the geometrical parameters and incidence characteristics to-gether. By using the multilayer algorithm, single cylindersare considered so as to investigate the subwavelength imag-ing and wave interaction. Different kinds of metamaterialsingle cylinders are studied. Interesting results such as fo-cusing properties and energy localization are shown. Next,we further study the cylinder with magnetoelectric couplingas a special case. In this case, the cylinder is character-ized by 3 parameters: permittivity, permeability and chi-rality. The effect of magnetoelectric coupling is presentedand resonant scattering is discussed. Finally, the cloaking ofcylinders and its effects on cross section are examined.

2. Preliminaries

2.1 Eigenfunction Expansion

Consider a parallel infinite line source with electric currentI, which is placed at (ρ0,φ0) from the cylinder as depictedin Fig. 1. The incident field due to the line source can beexpressed

Ei = − k2I4ωε0

∞∑n=0

(2 − δn0) H(1)n (kρ0) N(1)

n (k) e− jnφ0

(1)

Fig. 1 Cross-section view of a multilayered cylinder with the line sourcein 1st region.

Copyright c© 2007 The Institute of Electronics, Information and Communication Engineers

2424IEICE TRANS. COMMUN., VOL.E90–B, NO.9 SEPTEMBER 2007

Hi = − kI4 j

∞∑n=0

(2 − δn0) H(1)n (kρ0) M(1)

n (k) e− jnφ0

(2)

where the vector wave functions (VWFs) have been given in[13], [14]

N(1)n (k) = zJn(kρ)e jnφ (3)

M(1)n (k) =

[ρ

jnkρ

Jn(kρ) − φJ′n(kρ)]e jnφ. (4)

One can however note that the superscript of VWFs wouldchange to 3 if the multiple reflection and transmission aretaken into accout due to the interfaces in Fig. 1:

N(3)n (k) = zH(1)

n (kρ)e jnφ (5)

M(3)n (k) =

[ρ

jnkρ

H(1)n (kρ) − φH′(1)

n (kρ)]e jnφ. (6)

Based on the eigenfunction expansion, the electromagneticfields in intermediate layers (e.g., f th layer) are as follows

E f =

∞∑n=0

{an f N(3)

n

(kz f

)+ bn f M(3)

n

(kz f

)+ a′n f N(1)

n

(kz f

)+ b′n f M(1)

n

(kz f

) }, (7)

H f =1

jη f

∞∑n=0

{an f M(3)

n

(kz f

)+ bn f N(3)

n

(kz f

)+ a′n f M(1)

n

(kz f

)+ b′n f N(1)

n

(kz f

) }. (8)

In Eq. (7), scattering coefficients a′n f and b′n f denote incom-ing TM and TE modes (Bessel function being convergentapproaching the origin), and an f and bn f represent outgo-ing TM and TE modes (Hankel function being finite in theinfinity). Therefore, in the 1st region, the scattered electricfield only contains Hankel function. In Nth region, the scat-tered electric field only contains Bessel function. This isthe principle of eigenfunction expansion. In the intermedi-ate layers, the fields are just the superposition of inward andoutward scattered fields due to the multiple interfaces. Notethat kz f and η f = k f /ωµ f denote longitudinal wavenumberand wave impedance in f th layer, respectively. k2

f = ω2µ f ε f

is the wavenumber for incidence at arbitrary angles, and itreads k2

f = k2ρ + k2

z where kρ is the radial wavenumber in f thlayer.

Those scattering coefficients can be solved in a multi-layer algorithm associated with boundary conditions at eachinterface, which will be shown later. Thus, we can have theelectromagnetic field expansions based on the field couplingtogether with the incoming/outgoing waves superposition.The electric fields in 1st and Nth layer are given, respec-tively

E1 = Ei +

∞∑n=0

{an1N(3)

n (kz1) + bn1 M(3)n (kz1)

}(9)

EN =

∞∑n=0

{a′nN N(1)

n (kzN) + b′nN M(1)n (kzN)

}. (10)

Note that the vectors M(k) and N(k) have the following re-lations

∇ × M(k) = kN(k) (11)

∇ × N(k) = kM(k). (12)

Therefore, the magnetic fields in 1st and Nth can be obtainedas follows

H1=Hi+1

jη1

∞∑n=0

{an1 M(3)

n (kz1)+bn1N(3)n (kz1)

}(13)

HN =1

jηN

∞∑n=0

{a′nN M(1)

n (kzN) + b′nN N(1)n (kzN)

}. (14)

2.2 Multilayer Algorithm

The electromagnetic fields satisfy the boundary conditionsat each interface ρ = ρ f

ρ ×[

E f

H f

]= ρ ×

[E( f+1)

H( f+1)

]. (15)

Inserting Eqs. (7) and (8) into Eq. (15), we have a linearequation[

F f

] [C f

]=[F( f+1)

] [C( f+1)

](16)

where[F f

]is a 4 × 4 matrix

[F f

]=

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣F f 1

F f 2

F f 3

F f 4

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (17)

with the definition[F f 1

]=[

0 −H′(1)n (k f ρ) 0 −J′n(k f ρ)

][F f 2

]=[−H(1)

n (k f ρ) 0 −Jn(k f ρ) 0]

[F f 3

]=

[−H′(1)

n (k f ρ)jη f

0 − J′n(k f ρ)jη f

0]

[F f 4

]=

[0 −H(1)

n (k f ρ)jη f

0 − Jn(k f ρ)jη f

].

Note that the derivative is with respect to the argument. The[C f

]is a vector of unknown scattering coefficients

[C f

]=[

an f bn f a′n f b′n f

]T. (18)

By defining a new matrix[T f

]=[F f+1

]−1 [F f

], (19)

we can rewrite

[CN] =[T (1)

N

][C1] (20)

where[T ( f )

N

]=[TN− f

] [TN−( f+1)

]. . . [T2] [T1] . (21)

QIU et al.: ELECTROMAGNETIC SCATTERING PROPERTIES IN A MULTILAYERED METAMATERIAL CYLINDER2425

Therefore, the coefficient relationship between inner- andouter-most layer can be established⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

00

a′nNb′nN

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ =[T (1)

N

] ⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣an1

bn1

a′n1b′n1

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ . (22)

In view of Eq. (1), we have

a′n1 = − (2 − δn0)k2

1I

4ωε0H(1)

n (k1ρ0) e− jnφ0 , (23)

b′n1 = 0 (24)

where k1 is just the wave number in free space. Since a′n1and b′n1 are already known, an1 and bn1 can be determined

via the first two rows of[T (1)

N

]in Eq. (22), regardless of the

value of a′nN and b′nN . Provided [C1] is obtained,[C f

]is

straightforward by using Eq. (21). As a result, electromag-netic fields in any region can be formulated.

2.3 Magnetoelectric Coupling

To consider a more general case, the dielectric material isjust a subset of the bi-isotropic material, which exhibit mag-netoelectric coupling in the form of

D = εrε0E + jκ√ε0µ0H (25)

B = − jκ√ε0µ0E + µrµ0H (26)

where the chirality κ denotes the degree of magnetoelectriccoupling.

Lindell et al have presented the wavefield decompo-sition method in [15]. Instead of treating the electromag-netic problems in bi-isotropic media directly, the field com-ponents can be split into two partial fields

E = E+ + E− (27)

H = H+ + H− (28)

with a pair of equivalent isotropic mediums:

ε± = ε(1 ± κ) (29)

µ± = µ(1 ± κ). (30)

Hence, the previous formulated algorithm can still workeven for bi-isotropic media. As a special case, chiral ni-hility was proposed by Tretyakov et al. in [16] to achievebackward wave and negative refraction. Later on, Qiu et alstudied the energy transport in the chiral nihility and revis-ited the condition of chiral nihility for slabs in [17]. In thispaper, we further extend our study on chiral nihility to cylin-drical structures with the possibility of imaging and negativerafraction due to cylindrical curvatures. The chirality effecton subwavelength imaging will be discussed in detail in thefollowing section.

3. Results and Discussion

In this section, only one-layer and two-layer cylinders areconsidered because they possess enough interesting scatter-ing properties. The present work can be extended to study3-layer or 4-layer cylinders straightforwardly since the mul-tilayer algorithm developed above is suitable for arbitrarylayers.

3.1 One-Layer Isotropic Cylinder

First, let us investigate the scattering properties in the pres-ence of one-layer isotropic cylinder due to the line-sourceradiation. The material inside the cylinder in Fig. 2 is anti-vacuum (i.e, ε = −ε0 and µ = −µ0). The line source is placedat the position of (4.5λ, 0◦), which is very close to the sur-face of cylinder. As is known, a slab filled with anti-vacuumcan act as a perfect lens to focus light. However, if we con-sider perfect cylindrical lens, the parameters of the fillingmaterial must be dependent on the position. Nevertheless,partial focusing phenomenon can still be observed in Fig. 2.Also, some reflection can be observed at the positions be-hind the line source in Fig. 2 because of the cylindrical cur-vature. It can be seen that ripple occurs at the cylinder’ssurface close to the line source, which is the incoming win-dow of the incident wave. Certain points of this ripple carrycomparably high energy as the line source. In Fig. 3 andFig. 4, the line source is put further away to the cylinder’ssurface, while the radius of the cylinder keep unchanged.When the source is far away from the surface, the ripple ef-fect in the incoming window on the cylinder will be reducedas expected. In Fig. 3 and Fig. 4, foculas are formed due tothe imperfect focusing condition. By changing the positionof line source, the energy distributions outside the cylinderare greatly modified as can be seen from Fig. 2 to Fig. 4.It is due to the fact that when the line source is very closeto the cylinder’s surface, the curvature is quite flat withinthe incoming window of incident wave, which is close toslab configuration. If the line source is moved faraway, theincoming window becomes larger and the cylindrical curva-ture takes effect.

Fig. 2 Normalized magnitude of Poynting vector of a cylinder of a = 4λfilled with anti-vacuum and the line source at (4.5λ, 0◦).

2426IEICE TRANS. COMMUN., VOL.E90–B, NO.9 SEPTEMBER 2007

Fig. 3 Normalized magnitude of Poynting vector of the same cylinder asin Fig. 2 except the line source at (6λ, 0◦).

Fig. 4 Normalized magnitude of Poynting vector of the same cylinder asin Fig. 2 except the line source at (12λ, 0◦).

We further investigate scattering properties of sub-wavelength cylinders due to the line source radiation. Theradii in Fig. 5 and Fig. 6 are both equal 0.05λ, while thedistance of line source from the surface is 0.2λ and 1λ, re-spectively. Note that the energy distribution around the linesource is suppressed and only the distribution near the cylin-der is plotted. Two foculas with giant energy distribution arefound in Fig. 5 when the distance of line source from the sur-face is four times of the radius. Of particular interest is thatthe focula is not located inside the subwavelength cylinderany more. Instead, the foculas are formed in two particularareas around the cylindrical surface. If the distance of linesource increase to 20 times of radius (see Fig. 6), the magni-tude of the two foculas decrease and the positions are moreapart from each other.

3.2 One-Layer Bi-isotropic Cylinder

Now the bi-isotropic cylinder with magnetoelectric cou-plings, as described by Eqs. (25) and (26), is studied. Thedegree of magnetoelectric couplings is represented by thechirality of κ. Different chiralities are chosen so as to studythe effect of magnetoelectric coupling upon the scatteringproperties of the cylinder.

As a special case of bi-isotropic media, chiral nihility isconsidered first since it yields two special equivalent medi-ums: one is vacuum and the other is anti-vacuum, whichcan be verified in Eqs. (29) and (30). The judicious selection

Fig. 5 Normalized magnitude of Poynting vector of a cylinder of a =0.05λ filled with anti-vacuum and the line source at (0.25λ, 0◦).

Fig. 6 Normalized magnitude of Poynting vector of a cylinder of a =0.05λ filled with anti-vacuum and the line source at (1.05λ, 0◦).

of parameters for chiral nihility is based on the findings in[17]. It is shown in Fig. 7 that there are several foculas insidethe cylinder and both energy distributions inside and outsidethe cylinder are greatly modified by the existence of magne-toelectric couplings. Compared with Fig. 3, the energy inFig. 7 behind the cylinder is enhanced and those enhanceddistributions forms some ribbon-shaped areas.

In what follows, we consider normal bi-isotropic medi-ums with the same εr and µr, but different κ. The reason whyεr = µr is that the wave impedance of bi-isotropic mediumis independent of κ and identical with the impedance of freespace. From the comparison between Fig. 8 and Fig. 9, itcan be seen that the focusing appears more obvious for big-ger κ value. More interestingly, in Fig. 9, it not only presentstwo focusing points, but also enhance the energy inside thecylinder and high energy distribution is confined along thediameter.

3.3 Cloaking for Subwavelength Cylinders

Here the cloaking for a thin cylinder and its selection ofparameters are studied. We consider two combinations ofthe core and cloaking layers: double positive against doublenegative pair (DPS-DNG) and epsilon negative against munegative pair (ENG-MNG). Such combinations may giverise to the interface resonances, provided proper choice ofradii ratios. In analogy with what have been noticed for thinplanar resonators [18], [19], the condition of having a no-

QIU et al.: ELECTROMAGNETIC SCATTERING PROPERTIES IN A MULTILAYERED METAMATERIAL CYLINDER2427

Fig. 7 Normalized magnitude of Poynting vector of a bi-isotropic cylin-der of a = 2.5λ filled with chiral nihility medium of εr = 1e−5, µr = 1e−5,and κ = 1 and the line source at (4.8λ, 0◦).

Fig. 8 Normalized magnitude of Poynting vector of a cylinder of a =2.5λ filled with bi-isotropic medium of εr = 1, µr = 1, and κ = 2 and theline source at (4.8λ, 0◦).

Fig. 9 Normalized magnitude of Poynting vector of a cylinder of a =2.5λ filled with bi-isotropic medium of εr = 1, µr = 1, and κ = 4 and theline source at (4.8λ, 0◦).

cut-off propagation mode in a thin cloaking cylinder filledwith a pair of DPS-DNG or ENG-MNG layers, depends onthe ratio of the radii of the core cylinder (i.e., ρ2) and thecloaking layer (i.e., ρ1) instead of the sum of radii or theouter radius. As shown in Fig. 10, a cloaking cylinder con-sists of 2 layers (i.e., 3 regions). The radius of the cloak-ing is ρ1 and the radius of the core-cylinder is ρ2. The linesource is placed at (ρ0 = 0.8λ, φ0 = 0◦). The outer radius ofthe cloaking layer is fixed to be ρ1 = 0.01λ and scatteringcross section (SCS) is plotted against the radii ratio in orderto find resonances. SCS is defined as the ratio of the power

Fig. 10 Scattering cross section versus ratio of core layer over cloakinglayer in two pairs of combinations: DNG-DPS and DPS-DPS. The outerspace is free space.

Fig. 11 Scattering cross section versus ratio of core layer over cloakinglayer in two pairs of combinations: DNG-DPS and DPS-DPS. In the case ofDNG-DPS pairing, the cloaking layer is filled with DNG medium of (−3ε0,−2µ0), and in the case of DPS-DPS pairing, the cloaking layer is filled withDPS medium of (3ε0, 2µ0). The core layer remains the same DPS mediumof (2ε0, µ0) for both pairings.

scattered by the scatterer to the incident power per unit area

SCS =12 Re[Esca × Hsca∗]12 Re[Einc × Hinc∗]

(31)

In Fig. 11, the dash line refers to the case that both thecore and cloaking layers are DPS mediums. Hence, we cansee that the SCS is very small since the geometry of thisscatter is in subwavelength size. Note that the SCS of dashline is very close to zero, but not exactly zero because weplot DNG-DPS in the same figure as well. Interestingly,a resonant ratio can be observed for DNG-DPS pairing atρ2/ρ1 ≈ 0.331, where the SCS is significantly enhanced. Itis attributed to the polaritons which are supported by thispairing. It also shows that a proper cloaking on a subwave-length conventional cylinder can yield a comparably largescattering width similar to that obtained from very thickcylinder. Therefore, the scattering properties of a geomet-rically small cylindrical scatterer can be amplified up to abig scatterer, if the cloaking material and the ratio of radiiare properly chosen.

Analogous scattering properties are obtained for ENG-MNG cloakings. In the solid line in Fig. 12, core layer is

2428IEICE TRANS. COMMUN., VOL.E90–B, NO.9 SEPTEMBER 2007

Fig. 12 Scattering cross section versus ratio of core layer over cloakinglayer in two pairs of combinations: ENG-MNG and DPS-DPS. In the caseof ENG-MNG pairing, the cloaking layer is filled with ENG medium of(−3ε0, µ0), while core layer is occupied by MNG medium of (4ε0, −2µ0).In the case of DPS-DPS pairing, the cloaking and core layers are filled withDPS medium of (3ε0, µ0) and (4ε0, 2µ0), respectively.

a mu-negative cylinder while the cloaking is an epsilon-negative coating. Resonant ratio can be found at ρ2/ρ1 ≈0.152. In contrast to DNG-DPS pairing, the resonant scat-tering in Fig. 12 is not as sensitive to ratio as in Fig. 11. Bycoating a MNG subwavelength cylinder by an ENG cloak-ing, the scattering is still much amplified compared to DPS-DPS combination even if the radii ratio is smaller than theresonant ratio at about 0.152. However, when the inner ra-dius ρ2 of MNG core layer keeps increasing, the scatteringcross section will reduce to that of DPS-DPS combinationas the dash line in Fig. 12.

4. Conclusion

In this paper, a multilayer algorithm is proposed to studythe scattering properties of multilayered metamaterial cylin-ders by the radiation of a line source. The algorithm cantreat arbitrary layers with arbitrary filling dielectric materi-als. Both single isotropic/bi-isotropic subwavelength cylin-der and subwavelength cloaking cylinders are investigated.Focusing phenomena and enhanced resonant scattering arepresented.

Acknowledgments

The authors are grateful to the support from SUMMA Foun-dation in US and French-Singaporean Merlion Project. C.-W. Qiu is also grateful to the Joint PhD Degree Programmeoffered by National University of Singapore, in Singapore,and Supelec, in Paris, France.

References

[1] V.G. Veselago, “The electrodynamics of substances with simultane-ously negative values of ε and µ,” Soviet Physics Uspekhi, vol.10,no.4, pp.509–514, 1968.

[2] A. Lakhtakia, “Handedness reversal of circular Bragg phenomenondue to negative real permittivity and permeability,” Opt. Express,vol.11, no.7, pp.716–722, 2003.

[3] J.B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev.Lett., vol.85, pp.3966–3969, 2000.

[4] A. Grbic and G.V. Eleftheriades, “Overcoming the diffraction limitwith a planar left-handed transmission-line lens,” Phys. Rev. Lett.,vol.92, 117403, 2004.

[5] R.W. Ziolkowski and A.D. Kipple, “Causality and double-negativemetamaterials,” Phys. Rev. E, vol.68, 026615, 2003.

[6] C.W. Qiu, H.Y. Yao, L.W. Li, S. Zouhdi, and T.S. Yeo, “Backwardwaves in magnetoelectrically chiral media: Propagation, impedance,and negative refraction,” Phys. Rev. B, vol.75, 155120, 2007.

[7] J.B. Pendry, “Perfect cylindrical lenses,” Opt. Express, vol.11, no.7,pp.755–760, 2003.

[8] S.A. Ramakrishna and J.B. Pendry, “Spherical perfect lens: Solu-tions of Maxwell’s equations for spherical geometry,” Phys. Rev. B,vol.69, 115115, 2004.

[9] J.A. Kong, “Electromagnetic wave interaction with stratified nega-tive isotropic media,” Prog. Electromagn. Res., vol.35, pp.315–334,2002.

[10] L.W. Li, P.S. Kooi, M.S. Leong, L.W. Li, and S.L. Ho, “On theeigenfunction expansion of dyadic Green’s functions in rectangu-lar cavities and waveguides,” IEEE Trans. Microw. Theory Tech.,vol.43, no.3, pp.700–702, 1995.

[11] C.W. Qiu, L.W. Li, H.Y. Yao, and S. Zouhdi, “Properties of Faradaychiral media: Green dyadics and negative refraction,” Phys. Rev. B,vol.74, 115110, 2006.

[12] C.W. Qiu, H.Y. Yao, L.W. Li, S. Zouhdi, and T.S. Yeo, “Eigenfunc-tional representation of dyadic Green’s functions in multilayeredgyrotropic chiral media,” J. Phys. A, Math. Theor., vol.40, no.21,pp.5751–5766, 2007.

[13] C.T. Tai, Dyadic Green’s Functions in Electromagnetic Theory, 2nded., IEEE Press, Piscataway, NJ, 1994.

[14] L.W. Li, S.N. Lim, M.S. Leong, and J.A. Kong, “Vector wavefunction expansion for dyadic Green’s functions for cylindricalchirowaveguides: An alternative representation,” J. Electromagn.Waves Appl., vol.14, no.5, pp.673–692, 2000.

[15] I.V. Lindell, A.H. Sihvola, S. A Tretyakov, and A.J. Viitanen, Elec-tromagnetic Waves in Chiral and Bi-isotropic Media, Artech House,Boston/London, 1994.

[16] S. Tretyakov, I. Nefedov, A. Sihvola, S. Maslovski, and C. Simovski,“Waves and energy in chiral nihility,” J. Electromagn. Waves Appl.,vol.17, no.5, pp.695–706, 2003.

[17] C.W. Qiu, N. Burokur, S. Zouhdi, and L.W. Li, “Study on energytransport in chiral nihility and chirality nihility effects,” submitted toJ. Opt. Soc. Am. A, 2006.

[18] N. Engheta, “An idea for thin subwavelength cavity resonators usingmetamaterials with negative permittivity and permeability,” IEEEAntennas Wirel. Propag. Lett., vol.1, no.1, pp.10–13, 2002.

[19] A. Alu and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: Resonance, tunneling and transparency,” IEEE Trans.Antennas Propag., vol.51, no.10, pp.2558–2571, Oct. 2003.

QIU et al.: ELECTROMAGNETIC SCATTERING PROPERTIES IN A MULTILAYERED METAMATERIAL CYLINDER2429

Cheng-Wei Qiu was born in Zhejiang,China, on March 9, 1981. He received theB.Eng. degree from the University of Scienceand Technology of China, Hefei, China, in 2003.In August 2003, he was admitted by the PhDprogram in National University of Singapore(NUS) in Singapore. Currently, he is work-ing at Laboratoire de Genie Electrique de Paris-Supelec, under the NUS-Supelec Joint PhD Pro-gramme. His research interests are in the ar-eas of electromagnetic wave theory, composite

functional materials, and metamaterial antennas. He was the recipientof SUMMA Graduate Fellowship in Advanced Electromagnetics for Year2005. He was also the recipient of IEEE AP-S Graduate Research Award in2006. In 2007, he received the Young Scientist Travel Grant for ISAP2007in Niigata, Japan and Travel Grant for Metamaterial’07 in Rome, Italy.

Hai-Ying Yao received the B.Eng. degree in electronic engineering,and M.Eng. degree and Ph.D. degree both in Electromagnetic Field and Mi-crowave Technology all from University of Electronic Science and Tech-nology of China (UESTC), Chengdu, China, in 1996, 1999, and 2002, re-spectively. From April 2000 to October 2001, she worked at City Uni-versity of Hong Kong, as a Research Assistant. From December 2002 toSeptember 2004, she worked at High Performance Computations on En-gineered Systems Programme of Singapore-MIT Alliance (SMA) as a Re-search Fellow. Since Oct. 2004, she has been a Research Fellow with theDepartment of Electrical and Computer Engineering at the National Uni-versity of Singapore. Her current research interests include fast algorithmsand hybrid methods in computational electromagnetics, radio wave propa-gation and scattering in various media, and analysis and design of variousantennas.

Shah-Nawaz Burokur was born in Mau-ritius in 1978. He received the DEA (Master)degree in microwave engineering from the Uni-versity of Rennes1, France, in 2002. In 2005, hereceived the Ph.D. degree from the Universityof Nantes, France. His Ph.D. research worksdealt with the applications of Split Ring Res-onators (SRR) to microwave devices and anten-nas. From September 2005 to August 2006, hewas a post-doctoral research fellow at the Lab-oratoire de Genie Electrique de Paris where he

worked on chiral metamaterials. He is actually a post-doctoral research fel-low at the Institut d’Electronique Fondamentale (IEF) - University of ParisSud, France. His current research interests are in the areas of microwaveand applications of periodic structures, complex media, metamaterials andmetasurfaces, in the analysis of integrated planar and conformal circuitsand antennas. Dr. Burokur has been the recipient of the Young ScientistAward, presented by the Union Radio-Scientifique Internationale (URSI)Commission B, in 2005. He serves as reviewer of the IET Microwaves,Antennas and Propagation and the Journal of Electromagnetic Waves andApplications. He is currently a member of the European Network of Ex-cellence METAMORPHOSE.

Saıd Zouhdi received the Ph.D. degreein Electronics from the University of Pierre etMarie Curie, France, in 1994 and the Habilita-tion in Electrical Engineering from the Univer-sity Paris Sud, France in 2003. He has been withthe Laboratoire de Genie Electrique de Paris atSupelec. He is currently a Professor of electri-cal engineering at the University Paris Sud. Hisresearch interests include electromagnetic waveinteraction with complex structures and anten-nas, electromagnetics of unconventional com-

plex materials such as metamaterials, chiral, bianisotropic and PBG ma-terials, and optimization methods for various designs. He is an Editor ofthe journal Metamaterials. He has published over 100 journal papers, bookchapters, and conference articles. He has organized 2 NATO AdvancedResearch Workshops and organized and chaired various special sessions ininternational symposia and conferences, and has guest edited/co-edited 3special issues. He has co-edited the first book on metamaterials “Advancesin Electromagnetics of Complex Media and Metamaterials” Kluwer Aca-demic Publishers, in 2003. Prof. Zouhdi is a senior member of the IEEEAntennas and Propagation Society.

Le-Wei Li received the Ph.D. degreein electrical engineering from Monash Univer-sity, Melbourne, Australia, in 1992. In 1992,he was jointly affiliated with the Departmentof Electrical and Computer Systems Engineer-ing, Monash University, and the Department ofPhysics, La Trobe University, Melbourne, Aus-tralia, where he was a Research Fellow. Since1992, he has been with the Department of Elec-trical and Computer Engineering, National Uni-versity of Singapore (NUS), Singapore, where

he is currently a Professor and Director of the NUS Centre for Microwaveand Radio Frequency. From 1999 to 2004, he worked part time with theHigh Performance Computations on Engineered Systems (HPCES) Pro-gramme of SingaporeMIT Alliance (SMA) as an SMA Faculty Fellow. Hiscurrent research interests include EM theory, computational electromag-netics, radio wave propagation and scattering in various media, microwavepropagation and scattering in tropical environment, and analysis and de-sign of various antennas. Within these areas, he coauthored SpheroidalWave Functions in Electromagnetic Theory (Wiley, 2001), 45 book chap-ters, over 250 international refereed journal papers (of which over 70 pa-pers were published in IEEE journals and the remaining in Physical ReviewE, Statistical Physics and Plasmas Fluids Related Interdisciplinary Topics,Radio Science, Proceedings of the IEE, and the Journal of ElectromagneticWaves and Applications (JEWA), 31 regional refereed journal papers, andover 260 international conference papers. As a regular reviewer of manyarchival journals, he is an overseas Editorial Board member of the Chi-nese Journal of Radio Science, an Associate Editor of JEWA and the EMWPublishing book series Progress In Electromagnetics Research (PIER), andan Associate Editor of Radio Science. He is also on the Editorial Boardof the Electromagnetics Journal. Dr. Li has been a member of The Elec-tromagnetics Academy since 1998. He is an Editorial Board member ofthe IEEE Transactions on Microwave Theory and Techniques. He was thepast chairman of the IEEE Singapore Microwave Theory and Techniques(MTT)/Antennas and Propagation (AP) Joint Chapter during 2002C2003,during which time the 2003 IEEE Antennas and Propagation Society (IEEEAP-S) Best Chapter Award was presented to the Singapore Chapter. Hewas also the recipient of the 2004 University Excellent Teachers Awardpresented by NUS. He was also the recipient of several other awards.